How I could replicate this bumpy texture?
If you'd rather not spend the poly-budget until render-time, you could do it with a Cycles (only) displacement shader. The features seem to be following the topology, so you could U UV unwrap your object with the 'Reset' option. That will make all the quads occupy the whole 0-1 UV space.
For render-time displacement to work,at the time of writing, Cycles has to be set to 'Experimental', and the material has to be set to 'Displacement', or 'Displacement and Bump' in its Settings panel.
The object has to be subdivided sufficiently to resolve the displacement detail. However, Cycles can decide how much render-time subdivision is needed, on a per-pixel basis, by giving the object a Subdivision Surface modifier, and checking 'Adaptive'.
Then you can use this sort of shader-tree:

To get this sort of result:

The 'Subtract' and 'Multiply' nodes could be a vector 'Mapping' node, if you prefer, and the 'Vector Curves' could be a 'Color Ramp' node, if you'd find it easier to use.
EDIT: Thanks to commentary by @Chris, about problems he encountered with this tree, I think it would actually be easier to use RGB Curves than Vector Curves.. the 'C' combined adjustment becomes available.. it behaves better. Here's his .blend, given the easier set-up: